Panel data with heteroskedasticity and autocorrelation

[Samuel Lehtinen]

Hello and thank You in advance!

I have read this thread (https://www.statalist.org/forums/for...utocorrelation), and would like to ask for advice in a fairly similar case.

I have an unbalanced panel with 220 obs, 20 groups, and T=13. I have used a Hausman test to determine I should use FE

    Test:  Ho:  difference in coefficients not systematic

                  chi2(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =       95.48
                Prob>chi2 =      0.0000

I have then run the Woolridge test for autocorrelation (xtserial)

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,      19) =     11.289
           Prob > F =      0.0033

And finally the modified Wald test for heteroscedasticity (xttest3)

chi2 (20)  =    3888.34
Prob>chi2 =      0.0000

And it seems my panel suffers from both, autocorrelation and heteroscedasticity.

My question is, I have run the model with xtreg, fe robust as well as xtscc (because it was suggested in one "email chain" on stata website) and I get results with quite significantly different p-values on certain variables between these two regressions. I am unclear on whether if xtreg with robust is enough to solve the issues, or would xtscc be preferred.

Thank You in advance,
Sam

[Carlo Lazzaro]

Samuel:
welcome to this forum.
If there's no evidence of correlation across panels, you can go -xtreg, fe- with cluster/robust standard error.

[Samuel Lehtinen]

Thank you very much Carlo!

I am sorry to bother you a bit more, I ran xtcdf to test for correlation across panels and got the following results, which suggest there is correlation between panels.

------------------------------------------------------------------------------+
    Variable    |  CD-test   p-value   average joint T | mean ρ   mean abs(ρ) |
----------------+--------------------------------------+----------------------|
    LOGSTOCK    +  25.645     0.000         10.28      +  0.52       0.77     | 
   logGDPpCAP   +  27.203     0.000         12.90      +  0.52       0.77     | 
      ORE       +  5.604      0.000         11.03      +  0.08       0.42     | .
     RL_EST     +  -.824      0.410         13.00      +  -0.02      0.41     | 
      GDPG      +  19.952     0.000         12.90      +  0.38       0.41     | 
      INF       +  13.625     0.000         12.80      +  0.25       0.35     | 
    EXP_TO_H    +  26.721     0.000         13.00      +  0.51       0.57     | 
   IMP_FROM_H   +  7.096      0.000         13.00      +  0.14       0.44     | 
    logTRADE    +  15.148     0.000         12.90      +  0.29       0.44     | 
------------------------------------------------------------------------------+

Unfortunately my econometric/statistical knowledge leaves me a bit clueless at this point. Am I right in believing that using xtscc solves this issue, or do I need to look into alternative methodology to solve it?

Thanks!
Sam

[Firmin Clairant]

Dear Samuel,
Indeed, in case of cross section dependance, you can use xtscc. However, it will read some paper source Driscoll-Kraay (1998) "Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data". Here attached a table summarizing you a little under what conditions you can use it.

[Samuel Lehtinen]

Hi!

Thank you very much for your help! I found this Daniel Hoechle paper you have the table from, and it is very useful! Seems like running my regression with xtscc is the way to go! I will have a quick look at the original Driscoll & Kraay paper just in case there is something I should still consider.

Thanks!
Sam